Two famous Germans of the 19th Century, mathematician Carl Friedrich Gauss and explorer/geologist Alexander von Humboldt, are irreverently presented in this novel which topped the sales charts in Germany for more than a year.

With greater emphasis on the art of the story than an attempt to be true to the historical figures, Kehlmann presents both of these scientific "heroes" as uncaring jerks. Gauss' genius is exaggerated to the point that he can essentially see the future, predicting the downfall of the German monarchy when as a child he meets a Duke and foreseeing such inventions as airplanes and space based telescopes. Humboldt, because of his repressed sexuality (Humboldt is thought to have been gay, see here, for instance), comes across as being entirely anti-social.

The novel builds to a climax in which the two giants meet at a conference.

An excerpt from this novel was published as a short story, The Mathematician, in the Paris Review. It focuses on Gauss as a youth and displays this notion of "genius" which I find so disturbing. I appreciate that it is an attempt at the literary style known as "magical realism", but I fear that this reflects an honest misconception about how very intelligent people think.
It sets up Gauss as not simply a smart child, but one whose mental processes are so amazing, that even reading them today with 21st century hindsight they seem literally miraculous. For instance, in the story we see the boy:

Deduce non-Euclidean geometry (that "parallel lines meet") from a balloon flight in which he looks at the stars.

Predict the end of royalty in Germany upon meeting a Duke. (In fact, the historical Gauss was an ardent supporter of the monarchy.)

Conclude that the phlogiston theory of combustion is incorrect and that the light from flames is produced by the heating of the air around the fire by simply looking up at a candle.

The thing I object to here is that these conclusions seem to simply appear in his mind without any effort and (more importantly) without him having to have either knowledge or a logical way of deducing them. Certainly, if he had been presented as knowing more about history and political science, or had knowledge of experiments which suggested and supported Einstein's theory of relativity (not yet conducted when he was a child) or knew something of experiments that measure substances before and after combustion then perhaps these things would not be impossible...but in the story they are presented as being possible only because he is Gauss, as if his powers were supernatural.

The famous anecdote about his discovery that the sum of the integers from 1 to n is n*(n+1)/2 is repeated in this story. That, in fact, does not strike me as being impossible. Certainly, it requires great cleverness, but quite a few children are capable of exhibiting such cleverness as the champions of the many mathematics competitions demonstrate. Mostly, one merely needs the belief that it is possible to figure out a clever solution, and some experience with solving mathematical problems, and this particular formula is a reasonable discovery for a smart (but not "genius") child.

In fact, the view of genius presented in Measuring the World is much closer to my own when it describes Carl's reaction to his mother's lack of interest in learning to read. He concludes that most people just don't want to think. Conversely, I think that the people who make brilliant discoveries in science and math are (a) lucky to be in the right place at the right time and (b) have a strong desire to think and work on these sorts of questions. That, as opposed to a radically different way of thinking, is what makes a "genius" as I see it. Well, there is one other thing necessary to make a genius...and that is the desire of other people to mythologize and deify these people by telling stories about how different they are.

A review of this book by mathematician Frans Oort has been published in the AMS Notices (see here). Oort knows more about the real life of Gauss than I do, and so was even more bothered than I was by the liberties that Kehlmann took in presenting him as anti-social. For instance, while the novel presents Gauss as having barely noticed the death of his wife Johanna (he merely pauses momentarily from his work to think about the fact that he'd have to find another wife), Oort is able to quote from the letter that Gauss actually wrote to his friend Olbers: "Yesterday evening at 8 o'clock, I closed her angelic eyes in which I have found heaven for the last five years. Heaven gives me the strength to bear this blow. Give me a few weeks Olbers to gather new strength in the arms of your friendship..." Then, like me, Oort is concerned about the misimpression that the novel's portrayal will have on its readers. He says "Some people tell me that they are glad to have read a book that gives them this much information about Gauss, about whom they knew little before. This is the main problem. Readers take it for granted that the novel is well-researched, so that historical facts are correct and that psychological portraits are reasonably accurate. Not so in this novel..."